As part of responding to the first research question stated as: Research Question 1: (“Cog-nitive nodes:”) Can next generation mesh networks be designed to include Cognitive nodes that can learn from their environment and broadcast that information in order to allow the mesh network optimize its routing performance based on informed decision? can free spectrum be shared efficiently over spectrum sharing games?. In this section we carry-out a performance eval-uation of the cooperative spectrum sharing framework by using three different analytic models to demonstrate how spectrum can be shared cooperatively in different ways. Specifically we show through the design of a low cost heterogeneous Cognitive mesh network, how the Cognitive nodes will as part of cooperating, exchange and consolidate the information learned from the radio environment so as to optimize the payoff of the entire network system. Our heterogeneous system design is a Cognitive Radio Mesh Network Comprising of Integrated Wi-Fi and WiMAX Networks as shown in Figure 5.2 wherein the leader is engaged in an interactive game with the followers. For purposes of evaluation we envisage our Cognitive mesh to be having a leader entity (WS BS) with 20MHz of spectrum. In the next subsections we carry out the evaluation as follows. In subsection 5.9.1 we deal with the delay analytic model proposed in section5.6, this is followed by an evaluation of a throughput model in subsection 5.9.2 as proposed in section 5.7.
Finally the composite metric based model proposed in 5.8 is evaluated in subsection 5.9.3. In the Throughput and Composite models we make use of a genetic algorithm with the parameter settings in table 5.6.
Table 5.6: GA parameter setting
Parameter Value
Initialisation method Random Selection method roulette Crossover operation two point Mutation operation gaussian
Fitness Function Eqn 5.37, Eqn 5.8
Elitism 4
Population size (N) 100 Mating pool size 0.8*N Crossover probability 0.01 Number of iterations 50
5.9.1 Delay model. An evaluation of the QoS delay based model proposed in section 5.6 is carried out, starting from Figure 5.3 through to Figure 5.6. A variation of the SU demand with price levied by the White Space-BS is depicted in Figure 5.3in accordance with the predictions of equation 5.24. As the price levied by White Space-BS increases the demand for spectrum by the SU decreases, this is attributed to the Wi-Fi router passing on the costs to the Wi-Fi nodes by also imposing higher prices. Subsequently this impacts on the profit to be realized. The demand function is also investigated with variable number of nodes at the same price upon which there is a realization that there is a correlation between the number of nodes and the level of spectrum demand. The correlation is such that the higher the number of nodes the higher the demand for spectrum. In Figure 5.4, an investigation of the price dependency on arrival rate is carried out. Notably when the arrival rate is increased the price charged to the Wi-Fi routers must also increase.
Figure 5.3: Secondary User (SU) Spectrum Demand Dependence on Price Charged by WiMAX Base Station (BS)
The investigation is carried out for a variable of nodes ranging from 10 to 16 nodes. In view of this variation, it is important to note that at the beginning the curves representing the different node sets half nearly the same price of nearly 2.5 units. The difference in price then becomes apparent as the number of nodes vary so much such that, the more the number of nodes the greater the price charged. Furthermore the same investigation is extended to the bandwidth and arrival rate dependency as shown in Figure 5.5.
Figure 5.4: Arrival rate and its dependence on Price charged to Wi-Fi routers
Figure 5.5: Bandwidth Requirement Dependence on Arrival rate for Wi-Fi nodes
A smaller arrival rate is associated with a larger bandwidth and as the arrival rate increases the bandwidth requirement drops. However, for the same batch of node groups, a smaller group of
10 nodes has higher bandwidth requirement than a larger group of 16 nodes. Ultimately the variation in the arrival rate influences the price and subsequently the profit attained by the WS BS. The objective of the White Space BS is thus to maximize its profit derived from the leasing of its bandwidth with price being a fundamental variable in the equation 5.37. To this end, we focus on Figure 5.6 wherein the graph depicts the variation of profit of the White Space BS with price. The price regime is such that there are two prices P1 and P2 and the profit attained takes the form of a reverse Dijong shape. Finally the relation between the price and number of nodes is explored from equation 5.24, in Figure 5.7 with investigations revealing that there is a direct dependence between the price at equilibrium and number of nodes served.
Figure 5.6: Profit of the Base station (BS) and its dependence on prices
Figure 5.7: Price dependence on Number of Wi-Fi (SU) Nodes
The same investigation is extended to the bandwidth and number of routers and results indicate an increase in bandwidth is experienced with an increase in number of routers as shown in Figure 5.8.
Figure 5.8: Bandwidth variation with Number of User Nodes
5.9.2 Throughput. The throughput based model proposed in section 5.7 seeks to understand the influence and contribution of this QoS metric towards efficient TV white space exploitation and utilization by SUs and the benefits accrued by the PUs in allowing part of their spectrum to be utilized. Our analysis on the influence of this metric spans from Figure 5.9 to Figure 5.12.
Starting from the profit function, it takes the reverse De Jong form, the point at which the profit function is maximal is deemed to be the equilibrium point. A more practical approach in the form of a genetic algorithm optimisation briefly introduced in chapter 2 subsection 2.4.5 and detailed in chapter 3, section 3.1.2 is adopted. Specifically the genetic algorithm is deployed at the WiMAX and Wi-Fi APs to ascertain knowledge such as TVWS spectrum demand as well as price adjustment. The objective function is the profit function in Equation 5.37 with the parameters as in table 5.6. Clearly from a genetic algorithm perspective a more practical approach yields an equilibrium value after about fifty generations as shown in Figure 5.11. Compared to the theoretically predicted value in the reverse De Jong test function, the genetic algorithm attained value is lower. Intuitively, increasing the number of Wi-Fi nodes generates nearly the same amount of profit, this perhaps could be an indication of the costs being simple shared between the nodes.
A further analysis of the throughput QoS metric shows that it varies directly with bandwidth as predicted by equation 5.30this is to say as the bandwidth increases so is the achieved throughput and by the same token when the bandwidth decreases the throughput correspondingly decreases as shown in Figure 5.9. However, if the bandwidth is fixed and the number of users varied, an inverse relationship exists between throughput and number of nodes, the throughput is initially higher and seems to fall nearly in an exponential fashion as the number of users increase. Four
cases are simultaneously investigated with the bandwidth fixed at the values between 5MHz to 20MHz as the number of users increase, which in some way is an investigation of scaling as shown in Figure 5.10. As expected a high number of users are associated with a higher throughput and a lower number is associated with low throughput. The ideal thing to do is to acquire more bandwidth so as to sustain more nodes as the network scales
Figure 5.9: Interdependence between Throughput and available Bandwidth
Figure 5.10: Behaviour of Throughput with increasing number of users (Scaling)
It thus suffices to investigate the relationship between throughput and price since bandwidth and throughput are directly related as shown previously. Certainly as the price is increased the throughput also correspondingly increases as shown in Figure 5.12. The implication of this result
is that more has to be paid for more throughput. This further implies the QoS is price dependent as predicted earlier by theory, a subscriber will determine their QoS by their willingness to pay.
An exception to the rule is however noted at the price value of five which is suggestively an equilibrium value where the price is the same regardless of the network size given in this context.
Figure 5.11: Profit of BS at Nash Equilibrium Equilibrium using a Genetic Algorithm
Figure 5.12: Interdependence between Throughput and Price charged
5.9.3 Composite Metric. The composite metric model proposed in section 5.8 is the third and final model that has been studied and its performance evaluation spans from Figure 5.13 to Figure 5.18. With regards to the Composite QoS metric, the variation between bandwidth and arrival rate is initially investigated wherein it is revealed that the bandwidth generally drops with
the increase in the arrival rate. The initial values for the bandwidth are however a bit higher than those in the delay model. Furthermore investigations are further extended to the number of SU nodes to be supported and the behavioural pattern seems to match those of the Delay model.
Figure 5.13: Bandwidth variation with the arrival rate for Wi-Fi nodes (Composite metric)
The pattern is such that a high number of nodes require a lower amount of bandwidth and the smaller number of nodes requires a higher amount of bandwidth as shown in Figure 5.13. This variation could possibly be suggestive of the delicate balancing act that is required in this metric.
Since this is primarily a pricing problem, our focus is also extended to pricing and arrival rate relations as shown by Figure 5.14. To this end, the price is seen to increase with an increase in the arrival rate. This is however also further extended to a scenario of a variable number of nodes. The higher the number of nodes the higher the price as depicted by the curve forN = 16 and the lower the number of nodes the lower the price as depicted by the same curve forN = 10.
Since this is a pricing problem we investigate willingness to pay with regards to the composite metric (bits/s) with the outcome depicted in Figure 5.15. As the composite metric in bits/s increases the price correspondingly increases as predicted by equation 5.39. However in general, for a group of nodes as the composite metric increases the price also increases. Notably, though the composite metric seems to linearly increase with price, there is a common point which is suggestively an equilibrium point at which irregardless of the number of nodes, the price and thus the composite metric remains the same as shown by the point (10,5). Finally, network scaling with regards to the composite metric is investigated and the outcome depicted in Figure 5.17 and is consistent with the theoretical prediction CM ∝ √1n. As the number of users increases the composite metric output decreases almost in an exponential manner though in a much more steeper manner than the throughput scenario. This can possible be perhaps due to the delicate balancing act in achieving a trade-off between the delay and throughput. Finally in Figure5.18the profit of the Leader which is the BS is presented from a genetic algorithm perspective. Compared to the throughput metric the value of the profit is slightly lower and again this could possibly be attributed to the need for a balancing act in this kind of QoS metric.
Figure 5.14: Price dependence on the arrival rate for Wi-Fi nodes (composite metric)
Figure 5.15: Composite Metric variation with Price charged to Wi-Fi Secondary (SU) nodes
The composite metric is also dependent on the bandwidth and this dependence is depicted in Figure 5.16. A direct dependence is observed between the composite metric and the bandwidth, this is to say as bandwidth increases the output due to the composite metric increases.
Figure 5.16: Dependence of Composite Metric on Bandwidth requirements of Wi-Fi Nodes
Figure 5.17: Dependence of Network Throughput on Number of users (SU) from a Composite metric perspective-Scaling of Network
Finally, network scaling with regards to the composite metric is investigated and the outcome depicted in Figure5.17and is consistent with the theoretical predictionCM ∝ √1n. As the number of users increases the composite metric output decreases almost in an exponential manner though
in a much more steeper manner than the throughput scenario. This can possible be perhaps due to the delicate balancing act in achieving a trade-off between the delay and throughput. Finally in Figure 5.18 the profit of the Leader which is the BS is presented from a genetic algorithm perspective. Compared to the throughput metric the value of the profit is slightly lower and again this could possibly be attributed to the need for a balancing act in this kind of QoS metric.
Figure 5.18: Leader Profit from a Composite metric (Throughput+Delay) Perspective)